Highest Common Factor of 230, 1975 using Euclid's algorithm
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 230, 1975 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 230, 1975 is 5 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 230, 1975 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 230, 1975 is 5.
HCF(230, 1975) = 5
HCF of 230, 1975 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 230, 1975 is 5.
Highest Common Factor of 230,1975 is 5
Step 1: Since 1975 > 230, we apply the division lemma to 1975 and 230, to get
1975 = 230 x 8 + 135
Step 2: Since the reminder 230 ≠ 0, we apply division lemma to 135 and 230, to get
230 = 135 x 1 + 95
Step 3: We consider the new divisor 135 and the new remainder 95, and apply the division lemma to get
135 = 95 x 1 + 40
We consider the new divisor 95 and the new remainder 40,and apply the division lemma to get
95 = 40 x 2 + 15
We consider the new divisor 40 and the new remainder 15,and apply the division lemma to get
40 = 15 x 2 + 10
We consider the new divisor 15 and the new remainder 10,and apply the division lemma to get
15 = 10 x 1 + 5
We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get
10 = 5 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 230 and 1975 is 5
Notice that 5 = HCF(10,5) = HCF(15,10) = HCF(40,15) = HCF(95,40) = HCF(135,95) = HCF(230,135) = HCF(1975,230) .
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Frequently Asked Questions on HCF of 230, 1975 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 230, 1975?
Answer: HCF of 230, 1975 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 230, 1975 using Euclid's Algorithm?
Answer: For arbitrary numbers 230, 1975 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.